Commonly, high-selectivity intermediate frequency (IF) filters in radio frequencies have been realized as surface-acoustic wave (SAW) filters or as ceramic filters. In both these filters, the electric signal is converted to a mechanical wave that propagates in some mechanical resonator. When the mechanical resonance frequency is the same as the frequency of the electrical signal, the signal is amplified; otherwise, it is suppressed. The filter transfer characteristics are defined by the mechanical parameters of the resonator: its size, material, the mode of the mechanical wave in the resonator, etc. In SAW filters, the waves travel on the surface of some piezoelectric material like Lithium Niobate (LiNbO3), while in ceramic filters, piezoceramic is used as the resonator. Both types of filters have a stable frequency response with sharp cut-offs and narrow passbands, but both suffer from some disadvantages. Tolerances in mechanical construction, variations in dielectric permittivity, and real world manufacturing limitations often require adjustment of filter characteristics and operational tuning of filters to conform to stringent application performance requirements.
In some applications, SAW filters have been replaced by Film Bulk Acoustic Resonator (FBAR) filters. Similar to SAW filters, FBAR filters also employ mechanical resonance to achieve stable narrowband frequency response with sharp cut-offs. The mechanical resonator is a thin film layer, and the mechanical wave propagates in the bulk of the layer. Filters based on FBARs have several advantages over SAW and ceramic filters, including better temperature stability, smaller size, compatibility with existing silicon technology, higher operating frequency range, ability to handle higher power, better electrostatic discharge sensitivity, and higher quality factor (Q-factor).
An FBAR exhibits two resonance values: one series, fs and one parallel, fp. Behavior of an FBAR resonator across a range of frequencies is illustrated in FIG. 1c, which shows the reactance of the resonator vs. frequency. At the series resonant frequency, the reactance is 0; the resonator acts like a short circuit; and a signal passes freely through the resonator. At the parallel resonant frequency, the reactance goes to infinity; the resonator acts like an open circuit; and a signal is blocked by the resonator. As may be seen by analysis of the modified Butterworth-Van Dyke (MBVD) equivalent circuit, the resistances in the MBVD equivalent circuit are very small compared with the impedance of the other circuit elements, and they are often neglected in theoretical analyses. The relative distance between series and parallel resonance frequencies fs and fp is about 2-3% and the Q-factor of an FBAR varies between 300 and 2500.
Two basic structures are commonly used for creating FBAR filters: ladder and lattice. In a ladder filter structure, a number of resonators are connected in series, with a shunt resonator connected to ground between each two adjacent series resonators. The central passband frequency of the ladder FBAR filter is defined by the series resonance frequency fs,series of the series resonators and the parallel resonance frequency fp,shunt of the shunt resonators, which are all equal. Thus, the series resonators are equivalent to short circuits at this frequency, connecting the filter input directly with the filter output. The shunt resonators are equivalent to open circuits at the same frequency and have no effect. The gain of the circuit is equal to one, which is the maximum gain of the filter. The gain in a small vicinity around this frequency is close to 1, which forms the filter passband.
Ladder FBAR filters present several disadvantages. First, they require many resonators in order to achieve reasonable attenuation in the stopband. In addition, constraints on the parameters of the resonators often necessitate adding additional elements such as inductors and capacitors in order to properly adjust the resonance frequencies of each FBAR in the filter. A third disadvantage is that adjustment of the filter characteristics with capacitors and inductors is often inconvenient and complicated. Finally, ladder filters do not allow significant extension of the filter passband bandwidth. The passband bandwidth is limited by the series resonance of the shunt FBARs and by the parallel resonance of the series FBARs.
A lattice filter circuit using resonators is shown in FIG. 1a. A lattice filter circuit, or bridge circuit, employs two different pairs of identical resonators. The parallel resonance frequency of one pair of resonators, 130 and 140, must equal the series resonance frequency of the other pair of resonators, 150 and 160. When this condition is satisfied, the passband theoretically extends from the series resonance frequency of the 130-140 pair to the parallel resonance frequency of the 150-160 pair. (In practice, the passband in the real circuit is slightly narrower within that range.) The transfer function of the lattice filter is given by the formula:
                    H        =                              R            ⁡                          (                                                Z                  b                                -                                  Z                  a                                            )                                                          (                              R                +                                  Z                  a                                            )                        ⁢                          (                              R                +                                  Z                  b                                            )                                                          (        1        )                            where        Za is the complex impedance of each of the resonator pair 130-140 in FIG. 1a;         Zb is the complex impedance of each of the resonator pair 150-160 in FIG. 1a;         R is the resistance value of two identical resistors, 120 and 180, connected in the circuit in FIG. 1a. The attenuation of the filter is given by the formula a=−20 log10|H| (in dB).        
The suppression of the signal in the stopband is much greater in the lattice circuit than in a single or double stage ladder circuit. FIG. 2a is a graphical representation of the attenuation of a signal in a lattice filter as a function of signal frequency. FIG. 2b is a more detailed representation of attenuation vs. frequency within the passband. As can be seen in the graphs, signal attenuation of the lattice filter increases monotonically in the stopband. In the ladder filter, in contrast, signal attenuation peaks at the edge of the passband and then returns rapidly to very low values.
The lattice filter shown in FIG. 1a has two frequencies of minimum attenuation, one at the frequency f0=fpa=fsb, and the other at the frequency that satisfies the condition R=√{square root over (ZaZb)}, where R is the resistance of the filter circuit. At the frequency f0, resonators 130 and 140 are in parallel resonance, and resonators 150 and 160 are in series resonance. Thus, resonators 130 and 140 act as open circuits, and resonators 150 and 160 act as short circuits, and the filter input is directly connected to the filter output, producing a maximum signal. The resonator characteristics that determine the resonant frequencies thereby determine the first frequency f0.
The second frequency of minimum attenuation occurs because, neglecting power losses in the resonators, the complex impedances Za of resonator pair 130-140 and Zb of resonator pair 150-160 may be considered purely imaginary, as noted earlier. The imaginary component of the impedance values (reactance) of a resonator as a function of frequency is shown in the graph of FIG. 1c. Inside the frequency band fsa<f<fpb, the impedances of resonator pairs 130-140 and 150-160 have opposite signs, and their product ZaZb is thus real and positive within this frequency band. When the condition R=√{square root over (ZaZb)} is satisfied, the expression for filter transfer function becomes:
                    H        =                                            R              -                              Z                a                                                    R              +                              Z                a                                              =                                                    R                -                                  Z                  b                                                            R                +                                  Z                  b                                                      .                                              (        2        )            Since Za and Zb are both purely imaginary, the magnitude of H becomes
                              R          2                +                  Z          a          2                                      R          2                +                  Z          a          2                      ,or 1, at maximum (minimum attenuation of 0 dB). The value of the product ZaZb increases monotonically from 0 to infinity in the interval fsa<f<fpb. Thus, the condition R=√{square root over (ZaZb)} will be satisfied for some value of f. FIG. 2c is a graphical representation of the attenuation vs. frequency within the passband of a lattice filter at a particular resistance value, showing two different attenuation minima in the passband.
While the passband in a lattice filter can be tuned by adjusting the resistances of the circuit, there are several difficulties with using this technique. First, the resistances affecting attenuation in a lattice filter include resistance values external to the filter circuit, i.e., the source and load resistances 120 and 180 in FIG. 1a. These resistances are exterior to the input terminals 112 and 114, and the output terminals 176 and 178, respectively. As such, their values are not necessarily accessible for adjustment in most applications. Second, because the resistors are connected to different parts of the circuit, their coordinated variation would be difficult to achieve.
In filter design, filter response may also be shaped by creating transmission zeros, or frequencies at which input signals are completely blocked by the system. The monotonically increasing frequency response of the lattice filter in the stopbands is due to the lack of transmission zeros in its transfer function. The existence of transmission zeros depends on the parameters of the resonators used in the circuit; and, if necessary, transmission zeros can be created by an appropriate design of the filter. A lattice filter based on piezoelectric resonators can have two transmission zeros—one below the passband and another above the passband.
If a lattice filter is loaded by some resistance R, its input impedance is equal to R at the frequency which satisfies R=√{square root over (ZaZb)}. This property facilitates the connection of multiple lattice filters in cascade. The input impedance of the filter does not change significantly for the other passband frequencies, and the cascade connection of several lattice stages does not significantly increase the maximum passband attenuation.
A significant disadvantage of FBAR lattice filters is the large number of resonators, a minimum of four for a single stage lattice filter. In addition, each pair of resonators must have identical operating parameters. Similarly, tuning elements of a lattice filter that are parts of the filter circuit must also have identical operating parameters. The use of tuning elements outside of the lattice, suggested in some prior art, results in the tuning elements being applied to all resonators in the lattice and simultaneously changing the resonance frequencies of all resonators. Thus, it is impossible to independently tune the parameters of the longitudinal and of the crossed resonators, further complicating and reducing the flexibility of the tuning process.
Another disadvantage of such filters is evident in the creation of transmission zeros. Transmission zeros (attenuation poles) are created in lattice filters by proper choice of the parameters of the resonators, effectively, choice of the values of the elements of their equivalent circuits. However, elements added to tune the filter passband alter the equivalent circuit of the combination of the FBAR and the tuning elements, affecting the position of the transmission zeros. Thus, it is difficult to achieve independent tuning of the passband and concurrent placement of the transmission zeros.
In summary, designing thin film resonators to conform to application-related specifications is driven by requirements for precise control of the resonance frequencies, optimal connections, maximum Q-factors, and purity of the main resonance. The resonance frequency is affected by both the resonator and the electrode thicknesses, necessitating precise control over the thickness and properties of the layers during manufacture. The design of the electrodes further represents trade-offs between low sheet resistivity, efficient electromechanical coupling, and high acoustic quality of the materials used Limitations in manufacturing processes dictate the necessity of tuning the filters post-manufacture to conform to operating specifications. However, the tuning of resonance frequencies of identical resonators in conventional lattice filters is a complex procedure because the additional circuit elements must be matched and because other interactions of circuit elements are affected by the tuning process.
Therefore, a need exists to provide a filter that is less complicated to manufacture, with operating parameters that can be easily adjusted and tuned to conform to stringent application specifications. A need also exists to identify methods for tuning such a filter. The circuit and methods herein described address these deficiencies and related problems.